Write a^4 - 3a^2 + 9 - 7 as a product of two monic quadratics with integer coefficients.
+2669 We let \(b = a^2\).
We can simplfy the equation to: \(b^2 -3b+2\).
To factor, we need a pair of numbers that multiply to 2 and add to -3.
We see that the only pair satisfying this is -2 and -1.
Now, we can rewrite as: \(b^2 - b + 2b + 2\).
Factoring the first 2 terms and the last 2 terms seperately gives us: \(b(b-1) - 2(b-1)\).
We can add these to get: \((b-2)(b-1)\).
Can you take it from here?
